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High-spin $d^7$ Co(II) compounds have recently been identified as possibleplatforms for realising highly anisotropic and bond-dependent couplingsfeatured in quantum-compass models such as the celebrated Kitaev model. Inorder to evaluate this potential, we consider all symmetry-allowedcontributions to the magnetic exchange for ideal edge-sharing bonds. Though acombination of ab-initio and cluster many-body calculations we conclude thatbond-dependent couplings are generally suppressed in favor of Heisenbergexchange for real materials. Consequences for several prominent materialsincluding Na$_2$Co$_2$TeO$_6$ and BaCo$_2$(AsO$_4$)$_2$ are discussed.

Magnetic Couplings in Edge-Sharing High-Spin $d^7$ Compounds